Showing papers on "Elasticity (economics) published in 1971"

The elastic constants of the human lens

Abstract: 1. When the lens is spun around its antero-posterior polar axis in an apparatus designed for the purpose, high speed photography can be used to record its changing profile. By this method a variable radial centrifugal force can be applied to the lens which mimics the pull of the zonule.2. If the lens is not stressed at its centre beyond 100 Nm(-2) it behaves as a truly elastic body. When stressed beyond this limit visco-elastic strain is produced at its poles.3. The human lens has isotropic elastic properties at the extremes of life, but at the other times Young's Modulus of Elasticity varies with the direction in which it is measured.4. Young's Modulus of Elasticity of the lens varies with age, polar elasticity and equatorial elasticity, at birth being 0.75 x 10(3) and 0.85 x 10(3) Nm(-2) respectively, while at 63 years of age both are equal to 3 x 10(3) Nm(-2).5. A comparison of Young's Modulus of the young human lens with that of the rabbit and cat shows that the polar elasticity of the lenses of these animals was 5 times greater in the young rabbit, and 21 times greater in the adult cat. Equatorial elasticities of the rabbit and human lens were equal, while in the cat the equatorial elasticity was four times greater.6. A mathematical model showing the lens substance possessing a nucleus of lower isotropic elasticity than that of the isotropic elastic cortex surrounding it, accounts for the difference between polar and equatorial elasticity of the intact adult lens.7. The implications of these findings are discussed in relation to:(i) accommodation and the rheological properties of the lens;(ii) possible differences in the physical state of the lenticular proteins in the cortex and nucleus which may account for the senile variations in Young's Modulus of Elasticity in these regions of the lens;(iii) the loss of accommodation due solely to an increase in Young's Modulus of Elasticity of the lens between the ages of 15 and 60. This would amount to 44% of the total observed in vivo.

An Evaluation of 55 Cobalt Substituted Nitinol Wire for Use in Orthodontics

Abstract: The authors suggest that 55 cobalt substituted Nitinol wire be used in orthodontics by reason of its properties of elasticity and resistance to corrosion. The Nitinol wires are compared with single strand stainless steel and triple strand Twistflex wires.

Theory of elasticity of a multilayered medium

Abstract: Though the basic equations of the linear theory of elasticity are well known, it is rather cumbersome to evaluate the exact state of stress and displacement for a multilayered medium. In this paper we discuss a formal solution based on integral transforms and matrix analysis. Essentially the problem is reduced to the evaluation of some basic matrices and thus the calculation takes place in a clearly arranged way. Here we restrict ourselves to plane elastic and isotropic layers and use cartesian coordinates.

Elasticity and Equations of State of Olivines in the Mg2SiO4-Fe2SiO4 System

Abstract: Summary Presented first in this paper are the elasticity data of seven olivines as a function of pressure, temperature, and Fe/Mg ratio. The elasticity data include (i) P and S wave velocities and their first derivatives with respect to pressure and temperature, (ii) the shear and bulk moduli and their first pressure and temperature derivatives, and (iii) Poisson’s ratio and its pressure and temperature derivatives (all evaluated at zero pressure and at ambient temperature). The critical thermal gradients for density and for P and S wave velocities are presented for olivine with different Fe/Mg ratios. Also presented are the Debye temperature and Gruneisen’s parameters yG and 6, for olivine as a function of Fe/Mg ratio. Next, incorporating these elasticity data with theories, equations-of-state parameters of olivine and olivine-transformed spinel as a function of Fe/Mg are found. The equations of state of olivine are then presented; a pressure-volume-temperature (PVT) relation for olivine is examined as a function of temperature and Fe/Mg ratio. Finally, based on F. Press’s recent Monte Carlo solutions, the present elasticity data are related to the Earth’s upper mantle within the framework of a peridotitic model, Typically, for 100 Fo, 50 Fo, and 100 Fa olivines, values of density po (in g~m-~), the P and S wave velocities (in km s-’), the adiabatic bulk modulus K, (in mb) and its pressure derivative dKJdp, Gruneisen’s parameters yc and 6,, the Debye temperature OD (in OK), and the critical thermal gradients Gi, where i stands for density and P and S wave velocities, are as follows:

A study of human aortic distensibility with relation to atherosclerosis and aging.

Abstract: In 1960 a comparative study on coronary atherosclerosis of Caucasians in Boston and of Japanese in Kyushu, Japan was done by Gore, Nakashima, Imai and Whitel by means of Gore Tejada’s atherosclerotic index [in 1960]. There was a remarkable difference between these two groups. Bostonian coronary atherosclerosis was much severer than that of the Japanese. Japanese 7th decade arteries, for instance, had the atherosclerosis comparable to that of 5th decade of Bostonians. We had thought since that time, Japanese arteries were much younger than American arteries. But, there is a question: &dquo;Is the atherosclerosis proportionate to the index of arterial senility?&dquo; Statisticians report the increase of cardiac death in Japan. Increasing fat intake and increasing environmental stress are thought to be main causes for this increase. According to Sumiyoshi, Tanaka, Gore and Hirst2 (1965), however, the frequency of myocardial infarction in autopsy cases of Kyushu University in Japan is still 2.3% and less than one-tenth of Bostonian cases. It can not be thought that the Japanese atherosclerosis had become so different in these 5 years. Now, let us come back to the first question: &dquo;Is the atherosclerosis proportionate to the index of arterial senility?&dquo; Burton3 reported that arterial distensibility diminished with aging, but did not relate it to atherosclerosis. It is very interesting, but it is not clear whether he thought the arterial distensibility had different meaning from the intimal change, because Burton cited the definition of arteriosclerosis seen in Stedman’s medical dictionary (1953): &dquo;fibrous overgrowth, mainly of the inner coat of an artery, associated with degenerative changes in the middle coat causing thickening of the arterial wall with loss of elasticity and contractility.&dquo; We would like to know whether these two pathologic changes, the intimal changes and the loss of elasticity, are in the same category or not.

Elastic shear moduli and crystal stability at high P and T

Abstract: This paper presents new theoretical expressions for the elastic velocities (of a cubic or isotropic homogeneous solid) as functions of density and temperature (equations 7 and 8). These equations have been derived within the fourth-order anharmonic theory, i.e., the extension of the theory of lattice dynamics into the regime of finite strain, and they include implicitly the effects of noncentral forces, distant-neighbor interaction, and thermal vibration. Application of the equations to garnet, spinel, and olivine (considered as Voigt-Reuss-Hill isotropic bodies) confirms and lends rigor to the present consensus on the elasticity of the mantle. The equations indicate further that the observed instabilities of these materials under upper mantle conditions are not directly related to vanishing of an elastic modulus.

Specification Error Tests and Alternative Functional Forms of the Aggregate Production Function

Abstract: Tests for specification error are applied to a number of alternative production function models using aggregate U. S. manufacturing data by states for the year 1957. On the basis of the test results, the CES production function is tentatively chosen in preference to the Cobb-Douglas, variable elasticity, one form of the generalized production function, and a simple quadratic in capital and labor. The CES function estimated in this case gives indications of increasing returns to scale and of having an elasticity of substitution parameter greater than one.

Evaluation of certain physical properties of meat using a universal testing machine

Abstract: — The Instron tester served to evaluate physical properties of uncooked rabbit and beef muscle including work of rupture, breaking strength, break elongation elasticity and stress relaxation. These methods measure variations in muscle type, aging and post-mortem treatments comparably with shearing instruments. Shank showed higher tensile properties than tenderloin, less elasticity and lost more applied stress. With rabbit, the breaking force of longissimus dorsi unrestrained during rigor was .237 Ib/g ± 7.5% for samples 5.0 cm by 0.2–0.5 cm2 while restrained muscle gave .168 ± 9.9% and also exhibited higher elasticity and break elongation. Post-mortem aging decreased tensile properties and elasticity. Psoas muscle, characterized by more coextensive fibers, had higher tensile properties than longissimus dorsi.

Flow and rubber elasticity of polymeric systems

Abstract: The rheological properties of linear high molecular weight compounds at temperatures above their glass transition region and melting point are considered. When the deformation rates at steady flow conditions are increased high-elastic deformations are first observed, then a viscosity anomaly develops. The interrelation of these phenomena depends greatly on molecular weight distribution. Simple shear deformation processes at constant deformation rates are compared with those for uniaxial extension. The change in relaxation spectrum under continuous deformation of polymers is discussed. Attention is drawn to the presentation of rheological dependences in the form of master curves and it is shown that under simple shear the relaxation spectra of many polymeric systems change similarly. The forced transition of polymers from the fluid to the high elastic state due to an increase in shear rate has beesi studied. The phenomenon is distinct for high molecular weight polymers with narrow molecular weight distribution. It is accompanied by transition of steady laminar flow to slippage of the polymer along the capillary wall alternating with relaxation and adhesion to the wall. Slippage accelerates the output of polymer from the capillary by decimal orders. The effect of temperature on the phenomenon is estimated. The purpose of this lecture is to review the latest experimental studies of the rheological properties of linear polymers at temperatures above their glass transition and melting temperatures, carried out at the Laboratory of Rheology of the Institute of Petrochemical Synthesis of the USSR Academy of Sciences in collaboration with a number of industrial laboratories. The most important feature of rheological behaviour of polymeric systems is due to the combination of fluidity and high elasticity, i.e. to the ability to accumulate simultaneously unlimited irrecoverable and large recoverable deformations. However, while numerous papers have been devoted to measuring the viscosity of polymeric systems, information on their high elasticity, based on direct measurements, is very limited. The reason for this is that high-elastic deformations are estimated after unloading the samples. from their elastic recovery in time. This is much more difficult than measuring viscosity or normal stresses closely associated with high elasticity. At low shear rates and stresses there is a simple relationship1'2 between the first differential of normal stresses (P1 1—P22), shear stresses (r), high elasticity moduli (Ge) and high-elastic deformations (Ye). However, at shear 423 F G. V. YINOGRADOV stresses and rates () differing substantially from zero theory gives no correct predictions of the type of this bond. It is therefore necessary to determine it experimentally at least, especially if it can describe the properties not only of polymers with different molecular weight distribution (MWD), but also of their solutions. Naturally, this requires extensive measurements of the high-elastic properties of polymers and their solutions, as well as systematization of published data. Until recently most of the information on the rheological characteristics of polymeric systems pertained to simple shear and it will therefore be interesting to touch briefly on the peculiarities of behaviour of polymers during uniaxial extension. When considering the high-elastic properties of polymeric systems in the fluid state one is naturally interested in the peculiarities of their behaviour on passing into the high elastic state under the action of increasing deformation rates: this pertains primarily to the change in fluidity of polymeric systems upon such forced transition to the high elastic state. DEVELOPMENT OF HIGH-ELASTiC AND IRRECOVERABLE DEFORMATIONS Linear polymers display high elasticity simultaneously with a viscosity anomaly, when a continuous space network of macromolecular entanglements appears in them. This corresponds to the molecular weight reaching its critical value (Mcr) and to sharp enhancement of the dependence of initial viscosity (, = on this quantity. It was shown in ref. 3 for a series of polydisperse polybutadienes, that with M —' Mcr, '—* 0. This immediately Data for stationary shear flow Viscosity

Interfiber stresses in filamentary composites

Abstract: Theoretical and experimental results for the magnitude and distribution of interfiber stresses in a transversely loaded composite consisting of an elastic matrix reinforced with elastic fibers are presented. Interfiber stress distribution is also given for an in plane shear load condition. The mathematical model consists of uniformly spaced circular fibers in a square array. An approximate solution is obtained for the interfiber stresses. Theoretical results are compared with results of a photoelasticity investigation, Fil'shtinskii's rigorous elasticity solution for a plate containing rigid circular inclusions, and with results of a rigorous elasticity solution for a three-dimensional problem. The present approximate solution provides good agreement with the experimental results and with the theoretical results obtained by other authors. The method of solution presented can be used for predicting interfiber stresses in composites with various shape fibers arranged in arbitrary arrays, as well as for investigating interfiber thermal stresses, elasto-plastic deformations, and residual stresses.

Elastico‐Viscous Flow Near a Rotating Disk

Abstract: The Navier‐Stokes equations are solved numerically for the flow of elastico‐viscous fluid near a rotating disk by expanding the velocity components in powers of a small parameter K0*. The main effect of elasticity is to increase the magnitude of the velocity components and to decrease the magnitude of the turning moment on the disk.